Poisson sigma model over group manifolds

We study the Poisson sigma model which can be viewed as a topological string theory. Mainly we concentrate our attention on the Poisson sigma model over a group manifold G with a Poisson-Lie structure. In this case the flat connection conditions arise naturally. The boundary conditions (D-branes) are studied in this model. It turns out that the D-branes are labelled by the coisotropic subgroups of G . We give a description of the moduli space of classical solutions over Riemann surfaces both without and with boundaries. Finally we comment briefly on the duality properties of the model.